You can program the SPI memory using .bin file following the steps:
1. Open "Bitstream Settings", check "-bin_file*" checkbox and click OK.
2. Click on "Generate Bitstream" to generate your bit and bin file.
3. Open "Hardware Manager -> Open Target -> Open New Target..."
4. Add your memory. For this, right click on device (xc7a35t_0) -> Add Configuration Memory Device -> write on Search "S25FL032" -> click OK
5. Right click on the flash memory -> Program Configuration Memory Device -> add configuration file (.bin file) -> click OK
Here is a link to a "beta" version of the project at this dropbox link. From what I understand, it is a working project that just needs a little more work in terms of explanations about timing constraints. There are also some notes about the project that I was told to pass on: